An on-shell field \(h^{(t)}_{\alpha (n)}\)  is said to be partially masslessPartially massless fields have been studied in diverse dimensions for over 35 years, see [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]} for some of the earlier works.
Lagrangian models for partially massless fields in AdS\(_d\)  were constructed in [9]}, [10]}, [11]}, and in [12]}, [13]}
for the specific case of AdS\(_3\) .
with depth \(t\)  if, in addition to the conditions (REF ), the pseudo-mass satisfies
\(\rho \equiv \rho ^{(\pm )}_{(t,n)} = \pm n(n-2t)\mathcal {S}~,\qquad 1\le t \le \lfloor n/2 \rfloor ~. \) 
